Undulatory filament robot propulsion in granular beds

We will discuss complementary experiments and elastohydrodynamic models of an undulating elastic filament in frictional fluids inspired by slender limbless organisms that swim in water and burrow in sediment beds. Building on previous experimental work with magnetoelastic robots composed of a magnet attached to a slender filament-like body that show anguilliform locomotion in low friction environments [1], we demonstrate examples which can power through highly viscous fluids and inside granular beds. By using granular medium composed of transparent glass and polystyrene beads that have the same refractive index and that of the interstitial liquid, we measure the form and the speed of the undulating robots as a function of driving amplitude frequency, filament bendability and aspect ratio. A damped elastohydrodynamic model which considers the elastic bending, frictional drag, and dipole driving at the head is developed to calculate the shape and speed of the robot. We shall present a comparison between the experimental observations with the model which predicts speed that increases inversely as the elastic modulus of the filament and the effective viscosity of the medium as a function of the granular fluidity. The further effect of having a robot head that can carry cargo which is larger than the filament body will be also discussed.

[1]: Dynamics of magnetoelastic robots in water-saturated granular beds, A. Biwas, et al. Phys. Rev. Fluids 8, 094304 (2023).